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An Application of Metric Cotype to Quasisymmetric Embeddings

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Metric and Differential Geometry

Part of the book series: Progress in Mathematics ((PM,volume 297))

Abstract

We apply the notion of metric cotype to show that Lp admits a quasisymmetric embedding into Lq if and only if \( p\leq q \, {\rm or} \, q\leq p\leq 2\).

Mathematics Subject Classification (2000). 46B85 and 51F99.

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References

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Author information

Authors and Affiliations

  1. Courant Institute, New York University, 251 Mercer Street, New York, 10012, NY, USA

    Assaf Naor

Authors
  1. Assaf Naor
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Corresponding author

Correspondence to Assaf Naor .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of California, South Hall 6511, Santa Barbara, 93106, New Jersey, USA

    Xianzhe Dai

  2. , Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, 08854, New Jersey, USA

    Xiaochun Rong

Additional information

Dedicated to Jeff Cheeger for his 65th birthday

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Naor, A. (2012). An Application of Metric Cotype to Quasisymmetric Embeddings. In: Dai, X., Rong, X. (eds) Metric and Differential Geometry. Progress in Mathematics, vol 297. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0257-4_7

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